Abstract

In this paper, we present a modelling framework for cellular evolution that is based on the notion that a cell's behaviour is driven by interactions with other cells and its immediate environment. We equip each cell with a phenotype that determines its behaviour and implement a decision mechanism to allow evolution of this phenotype. This decision mechanism is modelled using feed-forward neural networks, which have been suggested as suitable models of cell signalling pathways. The environmental variables are presented as inputs to the network and result in a response that corresponds to the phenotype of the cell. The response of the network is determined by the network parameters, which are subject to mutations when the cells divide. This approach is versatile as there are no restrictions on what the input or output nodes represent, they can be chosen to represent any environmental variables and behaviours that are of importance to the cell population under consideration. This framework was implemented in an individual-based model of solid tumour growth in order to investigate the impact of the tissue oxygen concentration on the growth and evolutionary dynamics of the tumour. Our results show that the oxygen concentration affects the tumour at the morphological level, but more importantly has a direct impact on the evolutionary dynamics. When the supply of oxygen is limited we observe a faster divergence away from the initial genotype, a higher population diversity and faster evolution towards aggressive phenotypes. The implementation of this framework suggests that this approach is well suited for modelling systems where evolution plays an important role and where a changing environment exerts selection pressure on the evolving population.

A schematic representation of how a cell takes the micro-environment as an input which is then ultimately processed by the cell genotype which in turn decides on an output response which is the phenotype. The resulting cell phenotype then has the potential to modify the micro-environment thus setting up a possible feedback loop.

The layout of the initial network used in the agent-based model of tumour growth. The input to the network is the number of neighbours of the cell and the local oxygen concentration. The output of the network corresponds to proliferation (P), quiescence (Q) and apotosis (A), out of which the strongest is chosen.

The two upper panels show the spatial distribution of cells at t =20, 60 and 100. Proliferating cells are coloured red, quiescent green and dead cells are blue. We can see a clear difference in the morphology of the tumours in the low and high oxygen case. The lower panel shows the oxygen concentration in the low oxygen case.